Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11719435 | C2 | semidirect |
| 2. #11719432 | C2 | semidirect |
| 3. C13×#498 | C2 | semidirect |
| 4. #11718748 | C2 | semidirect |
| 5. #11718745 | C2 | semidirect |
| 6. #11718532 | C2 | semidirect |
| 7. #11718531 | C2 | semidirect |
| 9. #11718517 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 72. D104 | Q8 | semidirect |
| 90. D52 | C2×Q8 | semidirect |
| 98. C8×C13 | C2×Q8 | semidirect |
| 103. #498 | D13 | semidirect |
| 194. C13 | #3384 | semidirect |
| 220. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719435 | 2 |
| #11719432 | 2 |
| C13×#498 | 2 |
| #11718748 | 2 |
| #11718745 | 2 |
| #11718532 | 2 |
| #11718531 | 2 |
| #11718530 | 2 |
| #11718517 | 2 |
| C4×D104 | 2 |
| #11718340 | 2 |
| #3384 | 13 |